CLEVELAND — The Celtics have championship aspirations. And while the reality is that it might be too soon to think about that this year, it is also true that they are progressing rapidly.

And in addition to having superstars, championship teams are generally not rattled when moments they cannot control do not go their way.

Against the Cavaliers on Saturday night, the Celtics did not exude calmness. When a foul was called against them that they thought was unfair, they put their palms in the air or put their hands on their heads or ran to the official to complain more directly. When a foul was not called against Cleveland when they felt it should have been, their response was the same.

“When they went on their small runs, we were still complaining at the refs and wanting calls while they were getting out in transition and getting easy baskets,’’ Celtics point guard Isaiah Thomas said. “We’ve just got to learn from it. It’s definitely something we can control, and we’ve got to know those types of things can cost us games.’’

While the Celtics were griping, the Cavaliers were busy surging back from an 18-point first-quarter deficit, and they ultimately breezed to the finish for a 120-103 victory, snapping Boston’s five-game winning streak.

When faced with adversity, the Cavaliers did not sulk. They surged.

“The biggest thing for me was we didn’t drop our heads,’’ Cleveland coach Tyronn Lue said. “We didn’t pout. We continued to play and continued to fight, and the game changed for us.’’

The Celtics, meanwhile, could not hide their displeasure. After their bickering escalated in the third period, they were warned that their next complaint would result in a technical foul. A few moments later, Marcus Smart complained and received a technical foul. Jared Sullinger was whistled for one in the fourth quarter, too.

“We feel like we deserve some of the calls other teams get,’’ Sullinger said, “but we just have to move forward and understand we have to play regardless of however the officiating is going. We have to play.’’

“The championship-caliber teams, no matter what’s going on, they’re even-keeled,’’ Thomas said. “They try to stick with each other as much as possible. We kind of did the opposite tonight.’’

When the Celtics came here to Quicken Loans Arena one month ago, they walked out after completing a stunning comeback win that ended with Avery Bradley’s buzzer-beating 3-pointer.

So Saturday’s game offered a rare chance to win the regular-season series against the Eastern Conference’s top team. And early on, it looked like the momentum from their recent 5-0 homestand had carried over to Cleveland.

Boston’s shooters were scorching at the start, and the Cavaliers seemed dazed. The Celtics made six of their first seven shots, including all three of their 3-point attempts.

With 2:36 left in the first quarter Smart drilled another 3-pointer, and then Evan Turner added a turnaround jumper from the baseline just over a minute later, staking the Celtics to their largest lead, 35-17.

“We came out real confident,’’ Thomas said. “It turned around fast.’’

Boston’s reserves have picked up the starters after early struggles time and again this season. And perhaps there was something unfamiliar about playing with such a cushion. But in the second quarter Cleveland clawed back against the Celtics’ backups. The Cavaliers needed just 2 minutes 36 seconds to unfurl a 12-0 run, and they went into halftime with a 55-54 lead.

“We took the biggest hit they could give us and responded the best way we know how,’’ Cavaliers forward LeBron James said, “by defending and by sharing the ball.’’

James had 28 points, 11 rebounds, and 8 assists to pace Cleveland, which had eight players reach double figures in scoring. The Cavaliers shot 51.2 percent from the field overall.

On offense, the Celtics were not moving the ball as crisply, and on defense they were consistently out of position. And in the third quarter they grew noticeably frustrated with the officiating.

The Cavaliers used a 12-2 run that started in the third quarter and extended into the fourth to take a 95-83 lead.

The Celtics stayed within reach, as a pair of Tyler Zeller free throws made it 103-96, but Cleveland extended its lead with a 7-0 burst and the Celtics were never a threat again.

Thomas had 27 points to lead Boston and Sullinger added 17 points and 13 rebounds. The Celtics have thrived in the open court this season, but they were held to 6 fast-break points in this game.

“They kept scoring,’’ Thomas said of the Cavaliers. “We couldn’t get any stops. Usually we’ll get stops and get easy baskets and get going like that. We just couldn’t get any stops, and that’s what stopped us from making our run.’’

Adam Himmelsbach can be reached at adam.himmelsbach@globe.com.